Can anyone tell me how to solve this issue with rigging and mesh?
Fist thing, the scale is -1 on the X axis, so apply the scale of your object:

Once done, you need to check the normals, enable Face Orientation in the Viewport Overlays panel:

Blue show face normal orientation, red the opposite, as you can see the normals are flipped outside on the right arm. To recalculate the normals, go in Edit mode, select all and press AltN: